EmpiricalVariogram       package:RandomFields       R Documentation

_E_m_p_i_r_i_c_a_l (_S_e_m_i-)_V_a_r_i_o_g_r_a_m

_D_e_s_c_r_i_p_t_i_o_n:

     `EmpiricalVariogram' calculates the empirical (semi-)variogram of
     a random field realisation

_U_s_a_g_e:

     EmpiricalVariogram(x, y=NULL, z=NULL, data, grid, bin, gridtriple=FALSE)

_A_r_g_u_m_e_n_t_s:

       x: vector of coordinates

       y: vector of coordinates

       z: vector of coordinates

    data: vector or matrix of data

    grid: logical; if `TRUE' then `x', `y', and `z' define a grid;
          otherwise `x', `y', and `z' are interpreted as points

     bin: vector of ascending values giving the bin boundaries

gridtriple: logical. Only relevant if `grid==TRUE'. If
          `gridtriple==TRUE' then `x', `y', and `z' are of the form
          `c(start,end,step)'; if `gridtriple==FALSE' then `x', `y',
          and `z' must be vectors of ascending values

_D_e_t_a_i_l_s:

     Comments on specific parameters:

        *  `data': the number of values must match the number of points
           (given by `x', `y', `z', `grid', and `gridtriple').  That
           is, it must equal the number of points or be a multiple of
           it.  In case the number of data equals n times the number of
           points, the data are interpreted as n independent
           realisations for the given set of points. 

        *  `(grid==FALSE)': the vectors `x', `y', and `z', are
           interpreted as vectors of coordinates

        *  `(grid==TRUE) && (gridtriple==FALSE)': the vectors \
           code{x}, `y', and `z' are increasing sequences with
           identical lags for each sequence. A corresponding grid is
           created (as given by `expand.grid').

        *  `(grid==TRUE) && (gridtriple==FALSE)': the vectors `x', `y',
           and `z' are triples of the form (start,end,step) defining a
           grid (as given by `expand.grid(seq(x$start,x$end,x$step),
           seq(y$start,y$end,y$step), seq(z$start,z$end,z$step))')

        *  The bins are left open, right closed intervals, i.e.,
           (`b[i]',`bin[i+1]'] for i=1,...,`length(bin)'-1.  Hence, to
           include zero, `bin[1]' must be negative.

_V_a_l_u_e:

     The function returns `list(centers,emp.vario)' where `centers' are
     the central points of the bins and `emp.vario' gives the empirical
     variogram. Both elements are vectors of length `(length(bin)-1)'.

_A_u_t_h_o_r(_s):

     Martin Schlather, Martin.Schlather@uni-bayreuth.de <URL:
     http://www.geo.uni-bayreuth.de/~martin>

_S_e_e _A_l_s_o:

     `GaussRF' and `RandomFields'

_E_x_a_m_p_l_e_s:

       #############################################################
       ## this example checks whether a certain simulation method ##
       ## works well for a specified covariance model and         ##
       ## a configuration of points                               ##
       #############################################################
       x <- seq(0, 10, 0.5)
       y <- seq(0, 10, 0.5)
       grid <- TRUE
       gridtriple <- FALSE   ## see help("GaussRF")
       model <- "wh"         ## whittlematern
       alpha <- 2
       mean <- 1
       variance <- 10
       nugget <- 5
       scale <- 2
       method <- "TBM3"
       bins <- seq(0, 5, 0.001)
       repetition <- 20 ## by far too small to get reliable results!!
                        ## It should be of order 500,
                        ## but then it will take some time
                        ## to do the simulations
       param <- c(mean, variance, nugget, scale, alpha)
       f <- GaussRF(x=x, y=y, grid=grid, gridtriple=gridtriple,
                       model=model, param=param, meth=method,
                       n=repetition)
       binned <- EmpiricalVariogram(x=x, y=y, data=f,
                      grid=grid, gridtriple=gridtriple, bin=bins)
       truevariogram  <- Variogram(binned$c, model, param)
       matplot(binned$c, cbind(truevariogram,binned$e), pch=c("*","e"))
       ##black curve gives the theoretical values

